Simply put, a heuristic is our automatic brain at work. Here's an example: most people would agree that air travel is more dangerous than any other type of travel.
But they would be wrong. We actually have a 1 in 100 chance of dying in a car crash, but an almost 1 in 10,000 chance of dying in air and space transport incidents.
However, since airplane crashes come to mind more easily than car crashes, we think they are more common. This is the availability heuristic.
We make these errors in judgement all the time. Here's a list of heuristics and biases to get you started on exploring the many ways in which we are far less rational and far less correct in our thinking than we’d like to give ourselves credit for.